# Maximal compatible splitting and diagonals of Kempf varieties

Niels Lauritzen^{[1]}; Jesper Funch Thomsen^{[1]}

- [1] Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark)

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 6, page 2543-2575
- ISSN: 0373-0956

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topLauritzen, Niels, and Thomsen, Jesper Funch. "Maximal compatible splitting and diagonals of Kempf varieties." Annales de l’institut Fourier 61.6 (2011): 2543-2575. <http://eudml.org/doc/219739>.

@article{Lauritzen2011,

abstract = {Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.},

affiliation = {Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark); Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark)},

author = {Lauritzen, Niels, Thomsen, Jesper Funch},

journal = {Annales de l’institut Fourier},

keywords = {Special linear group; Schubert variety; Frobenius splitting; maximal multiplicity; Wahl’s conjecture; Wahl's conjecture},

language = {eng},

number = {6},

pages = {2543-2575},

publisher = {Association des Annales de l’institut Fourier},

title = {Maximal compatible splitting and diagonals of Kempf varieties},

url = {http://eudml.org/doc/219739},

volume = {61},

year = {2011},

}

TY - JOUR

AU - Lauritzen, Niels

AU - Thomsen, Jesper Funch

TI - Maximal compatible splitting and diagonals of Kempf varieties

JO - Annales de l’institut Fourier

PY - 2011

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 6

SP - 2543

EP - 2575

AB - Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.

LA - eng

KW - Special linear group; Schubert variety; Frobenius splitting; maximal multiplicity; Wahl’s conjecture; Wahl's conjecture

UR - http://eudml.org/doc/219739

ER -

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